فهرست نشریات علمی دسترسی آزاد ایران

‎Pseudo-analysis has applications in several fields‎, ‎including game theory and optimization problems‎. ‎Pseudo-analysis is a generalized form of ordinary classical analysis that has two main operations‎. ‎In fact‎, ‎these two operations‎, ‎which are called pseudo-multiplication $\otimes$ and pseudo-addition $\oplus$‎, ‎are the basis of the formation of a semi-ring on the interval [c,d] of $ [-\infty,\infty]$‎. ‎The pseudo-operations $\otimes$ and $\oplus$ on [c,d] produce three types of semi-ring‎. ‎First‎, ‎the semi-ring $([c,d],\sup,\otimes)$ or $([c,d],\inf,\otimes)$ in which $\otimes$ is generated‎, ‎the second‎, ‎a semi-ring where $\otimes$ and $\oplus$ are defined by the continuous and strictly monotone function $\psi$‎, ‎the third‎, ‎a semi-ring in which both pseudo-operations $\otimes$ and $\oplus$ are idempotent‎. ‎In this article‎, ‎we intend to state and prove some of the most recent generalizations of Carleman-Knopp's type inequalities via pseudo-integrals‎.